Singularities play an important role in many areas of algebraic geometry.
For instance, singular varieties naturally appear in the minimal model program and in the study of moduli spaces, where it often happens that smooth objects degenerate to singular ones.
However, many classes of singularities that naturally occur are mild and can sometimes be understood in detail.
One of the natural classes of singularities is (log) canonical singularities.
These singularities have been extensively studied, especially in the case of surfaces.
In particular, we have a full classification of log canonical surface singularities.
(For a reference, see [1]}, [2]}, or [3]}.)
